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CALC (TANGENT LINE)

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1-show that 1-x/2 is the tangent line approximation to 1/ sqrt of 1+x near x=0

2-what is the local linearization of e^x^2 near x=1

3-find the tnagent line approximation of 1/x near x=1

  • CALC (TANGENT LINE) -

    1-show that [1-x]/2 is the tangent line approximation to 1/ sqrt [1+x] near x=0
    ------------------------------
    f(x) = (1+x)^-.5
    f'(x) = -.5(1+x)^-1.5
    series expansion(Taylor, Maclaurin)
    f(x) = f(0) + f'(x)*x/1! + ......
    f(x) = (1/2)(1+0)^-1.5 - .5(1+0)^-1.5 *x^1 + ...
    = 1/2 - x/2 + ...
    = (1-x)/2
    Now try the others yourself.

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